Linear Regression

If the regression line of $y$ on $x$ is $y = a$, then $b_{yx}$ is:

If $b_{yx} = b_{xy} = r$, then the standard deviations of $x$ and $y$ must be:

What is the relation between $b_{yx}$ and $r$ if $\sigma_x = 2\sigma_y$?

The regression line of $y$ on $x$ passes through the origin if:

The regression lines pass through $(10, 20)$. This implies:

If $b_{yx} = 0.8$ and $b_{xy} = 0.45$, find $r^2$.

The two regression lines are $y = 0.4x + 2$ and $x = 0.9y + 3$. The correlation coefficient is:

If the regression lines make angles $\alpha$ and $\beta$ with the positive $x$-axis, where $\alpha$ is for $y$ on $x$ and $\pi/2 - \beta$ is for $x$ on $y$ with respect to the $y$-axis, find $r^2$ in terms of $\alpha$ and $\beta$.

In a distribution where the line of regression of $y$ on $x$ is $y = 5 - 1.5x$ and the line of regression of $x$ on $y$ is $x = 10 - 0.5y$, find $r$.

If $b_{yx} = 2.5$ and $b_{xy} = 0.1$, which of the following is the coefficient of determination?

If the regression coefficient of $y$ on $x$ is $b_{yx} = 0.6$ and the standard deviations of the variables are $\sigma_x = 10$ and $\sigma_y = 12$, what is the value of the correlation coefficient $r$?

If $b_{yx}$ is positive, then $b_{xy}$ must be:

Linear regression analysis assumes that the relationship between the variables is a:

If $r^2 = 0.81$, then the magnitude of the correlation coefficient $|r|$ is:

If $b_{yx} = -1.2$ and $b_{xy} = -0.3$, which of the following is the correct value of $r$?

If the product of the regression coefficients is 1, then the correlation between variables is:

If the regression lines are $x + 2y - 5 = 0$ and $2x + 3y - 8 = 0$, find the mean of $x$.

The two regression lines are $y = 0.8x + 5$ and $x = 0.45y + 2$. Calculate the ratio of variance of $x$ to variance of $y$.

Given $b_{yx} = 0.85$ and $b_{xy} = 0.89$, find the value of $r$.

If the regression line of $y$ on $x$ makes an angle of 30^\\circ with the $x$-axis and the regression line of $x$ on $y$ makes an angle of 60^\\circ with the $x$-axis, find $r$.

The value of $r^2$ ranges between:

If the two regression coefficients are $b_{yx} = 4$ and $b_{xy} = 1/9$, then $r$ is:

If $r = -1$, the two regression lines:

If the sum of squares of $x$ deviations $\sum(x-\bar{x})^2 = 50$ and $\sum(x-\bar{x})(y-\bar{y}) = 25$, find $b_{yx}$.

If $r = 0.5$, then the ratio of the regression coefficient $b_{yx}$ to $b_{xy}$ is equal to:

If the line of regression of $y$ on $x$ is $y = 1.5x + 0.5$ and the line of regression of $x$ on $y$ is $x = 0.6y + 0.1$, the value of $r^2$ is:

Why are there usually two lines of regression?

In a bivariate study involving $20$ pairs of observations, the line of regression of $y$ on $x$ is $y = 2.5x + 7$ and the line of regression of $x$ on $y$ is $x = 0.1y + 4$. Given that the variance of $x$ is $4$, find the sum of the squares of the residuals (errors) for the regression of $y$ on $x$.

For the line $y = a + bx$ to be a valid regression line of $y$ on $x$, if the correlation $r$ is positive, the value of $b$ must be:

If $b_{yx} = 1.6$ and $b_{xy} = 0.4$, find the ratio $\sigma_y / \sigma_x$.

If $b_{yx} = 1.5$ and $r = 0.75$, find the value of the ratio $\sigma_x / \sigma_y$.

If $b_{yx} = 0.6$ and $r = 0.6$, what is the value of the regression coefficient $b_{xy}$?

If the product of the two regression coefficients is $0.49$ and both coefficients are negative, find the value of the correlation coefficient $r$.

If $b_{yx} = 3/2$ and $b_{xy} = 1/6$, what is the value of $r$?

If the regression coefficient $b_{yx}$ is $0.6$ and $x$ is multiplied by $2$ while $y$ is multiplied by $3$, the new regression coefficient $b'_{yx}$ will be:

If $b_{yx} = k$ and $b_{xy} = 1/k$ for some positive constant $k$, then $r$ must be:

When the correlation coefficient $r$ is $\pm 1$, the two regression lines are:

If $b_{yx} = 0.8$ and $b_{xy} = 0.2$, find the value of $\tan \theta$ if the ratio of standard deviations is $\sigma_y : \sigma_x = 2 : 1$.

In a bivariate data set, if $\sum x = 50, \sum y = 60, n = 10, \sum xy = 350, \sum x^2 = 300$, calculate the value of $b_{yx}$.

If $b_{yx} = 1.2$ and $b_{xy} = 0.3$, find the coefficient of correlation for the variables $U = 3x-2$ and $V = 5-2y$.